Ideal gases

Contents

• 15.1 Ideal Gas Law

  • 15.1.1 The Mole

  • 15.1.2 Ideal Gases

  • 15.1.3 Ideal Gas Equation

• 15.2 Kinetic Theory

  • 15.2.1 Kinetic Theory of Gases

  • 15.2.2 Derivation of the Kinetic Theory of Gases Equation

  • 15.2.3 Average Kinetic Energy of a Molecule

15.1 Ideal Gas Law

15.1.1 The Mole

• Amount of substance measured in moles (mol).

• Defined as containing the same number of particles as there are in 12 g of carbon-12.

• 1 mole of any element = relative atomic mass (in grams).

15.1.2 Ideal Gases

• Ideal gas: obeys the relation pV ∝ T.

• Molecules move randomly at high speeds.

• Higher temperature = faster molecules = more pressure.

• Pressure defined by collision frequency of gas molecules.

15.1.3 Ideal Gas Equation

• Ideal gas law: pV = nRT.

• p = pressure (Pa), V = volume (m³), n = number of moles, R = gas constant, T = temperature (K).

15.2 Kinetic Theory

15.2.1 Kinetic Theory of Gases

• Assumptions:

  • Gases consist of identical, elastic molecules.

  • Volume of molecules negligible compared to container volume.

  • Continuous random motion without intermolecular forces.

15.2.2 Derivation of the Kinetic Theory of Gases Equation

• Derives pressure from momentum change during collisions.

• Momentum change leads to force, contributing to overall pressure.

15.2.3 Average Kinetic Energy of a Molecule

• Average kinetic energy related to temperature: E ∝ T.

• Monatomic gases only have translational energy; diatomic gases have translational and rotational.